Full exam for Control and Actuating Devices for Mechanical Systems in the Mechanical Engineering degree programme at Politecnico di Milano. The document covers: CONTROL AND ACTUATING DEVICES FOR MECHANICAL SYSTEMS 11.01.2021 Consider the mechanical system represented in the figure placed in the vertical plane. A bar of length 3L, with mass π1 and moment of inertia π½1, slides without friction on a horizontal plane and is connected to
Full exam for Control and Actuating Devices for Mechanical Systems in the Mechanical Engineering degree programme at Politecnico di Milano. The document covers: CONTROL AND ACTUATING DEVICES FOR MECHANICAL SYSTEMS 11.01.2021 Consider the mechanical system represented in the figure placed in the vertical plane. A bar of length 3L, with mass π1 and moment of inertia π½1, slides without friction on a horizontal plane and is connected to
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CONTROL AND ACTUATING DEVICES FOR MECHANICAL SYSTEMS 11.01.2021 Consider the mechanical system represented in the figure placed in the vertical plane. A bar of length 3L, with mass π1 and moment of inertia π½1, slides without friction on a horizontal plane and is connected to the rod of a hydraulic actuator by a spring-damper group characterized by stiffne ss π1 and damping coefficient π1. The piston of the hydraulic actuator has a mass equal to ππ. A disc with mass ππ, moment of inertia π½π and radius R is pinned to the ground is its centre and is in contact with the bar. The contact is such that slippage is prevented. A bar with length 2L, mass π2 and moment of inertia π½2 is hinged to the disc at one end, while is connected to a massless beam on the other end. Such beam is connected to the ground both with a pin and with a torsional spring-damper group with torsional stiffness ππ and damping coefficient ππ. All the moments of inertia are computed with respect to the centre of mass. Consider the elongations of the springs to be null in the configuration depicted in figure. Consider the actuator as ideal (Ξ²ββ) and the spring K1 as completely rigid (k1ββ): Collect only the required information (in red) into a single document and upload it before the end of time defined for the first block. Write the equation of motion of the system and linearize it around the static equilibrium position depicted in the figure (ο± = 0). 1. Linearized equation of motion, indicating the equation of the generalized mass, damping, stiffness and external force. 2. Stability analysis Apply a Proportional-Derivative control on the rotation π of the beam acting on the displacement of the spool valve. 3. Linearized equation of motion, indicating the equation of the generalized mass, damping,β¦
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